tag:blogger.com,1999:blog-5324120177673194522.post1787699278370391615..comments2017-08-08T18:51:20.293-05:00Comments on Math Without Tears: Division of Fractions, Part 2; Real Life Problems for Division of Fraction StudyConcerned Teacherhttp://www.blogger.com/profile/06758529063793725123noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-5324120177673194522.post-29455584651760772232013-01-10T07:00:47.338-06:002013-01-10T07:00:47.338-06:00Hey! Have you ever thought, have your writting ski...Hey! Have you ever thought, have your writting skills upgraded recently?L. Morrishttp://lillianmorris20.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-75692313928185167162011-12-02T09:21:40.342-06:002011-12-02T09:21:40.342-06:00@ Concerned teacher:
I see an issue in telling ki...@ Concerned teacher:<br /><br />I see an issue in telling kids to think (how many_ are in_?)in that your problems are all quotative. <br />How would you ask your students to think about a partitive division of fractions problem? Consider the following example:<br /><br />I have 2/3 of a tank of gas but it is only enough to get me 3/4 of the way to my destination. How many tanks of gas do I need?Garyhttps://www.blogger.com/profile/01189861113865699360noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-70339951051121199252009-08-30T22:08:45.546-05:002009-08-30T22:08:45.546-05:00Anonymous: Great question!
For the problem 1/2 div...Anonymous: Great question!<br />For the problem 1/2 divided by 1 1/2, reread the problem: <br /><br />"How much of 3/2 is in 1/2?" as Saxon teaches students to reread problems.<br /><br />#1 Real life problem: How much of 1 1/2 (3/2) cups goes into a 1/2 Cup mold? <br />#2 problem: How much of the 1 1/2 gal. of gasoline goes into the 1/2 gal. tank? <br /><br />Using the reciprocal, shows that it's 1/3 of the 1 1/2 Cups or gal.<br /><br /><br />Hope this helps?Concerned Teacherhttps://www.blogger.com/profile/06758529063793725123noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-77477040437391808972009-08-30T21:05:54.986-05:002009-08-30T21:05:54.986-05:00Please advise on a real life situation where we ha...Please advise on a real life situation where we have to divide a fraction(Say 1/2) by a mixed fraction (1 and 1/2 =3/2)?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-23770097987482983832008-07-31T23:52:00.000-05:002008-07-31T23:52:00.000-05:00Thanks, Barry, so much for all of your insights.Thanks, Barry, so much for all of your insights.Concerned Teacherhttps://www.blogger.com/profile/06758529063793725123noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-3120442448091076342008-07-31T18:04:00.000-05:002008-07-31T18:04:00.000-05:00Also a technique to reinforce what dividing by fra...Also a technique to reinforce what dividing by fractions means, is to ask them how many nickles in a quarter? And how did they arrive at the answer? Easy: 25/5<BR/><BR/>Well let's change units. Instead of a quarter = 25 cents, a quarter = 1/4 of a dollar. And a nickle is 1/20 of a dollar. Now. How many 1/20ths are in 1/4?Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-33891924834793102192008-07-26T08:34:00.000-05:002008-07-26T08:34:00.000-05:00Yes, Barry. I love the manner that Saxon teaches ...Yes, Barry. I love the manner that Saxon teaches division of fractions. In fact, I've taught Saxon Math for many years and that is the next step we used. Once students understand they are really looking for "how many ____ are in ____?", they easily learn the process you have described. <BR/><BR/>The number 1 divided by a fraction is always it's reciprocal. How they love reciprocals! It's like playing with math!!! I take the students through the steps you have explained. We substitute 1(one) for the first fraction to get a reciprocal. I then always have the students "red flag" the reciprocal. Then we go back to our original first fraction. Since we are looking for 2/3 of 1/2, we want 2/3 of whatever answer we get, in this case 2 (which is flagged). We then work 2/3 of 2. <BR/><BR/>At first students think they are to go through all of those steps, until they suddenly catch on that they are using a reciprocal. Then I show them that we will just take a short cut and use go right to a reciprocal to solve every problem. <BR/><BR/>BUT having them learn to mentally reword the problem (how many ___ are in ___?) helps them because they can quickly reason through many problems, such as "how many 1/4's are in 3/2?" without even using the reciprocal. They know how to reword it and how to "think" through it. <BR/><BR/>Many a time, I'll ask a student how they got an answer without using a reciprocal, and they will say, well I knew how many 2/3 are in 3, so I know how many there are in 6, (or whatever the problem was). <BR/><BR/>Yes, 5th graders can learn division of fractions. They can understand what it means, and they can learn to use the reciprocal. Thank you Saxon.Concerned Teacherhttps://www.blogger.com/profile/06758529063793725123noreply@blogger.comtag:blogger.com,1999:blog-5324120177673194522.post-23566213338707848422008-07-26T06:41:00.000-05:002008-07-26T06:41:00.000-05:00Saxon Math has an interesting approach to teaching...Saxon Math has an interesting approach to teaching division by fractions. First they teach about reciprocals of fractions. Since students have learned about multiplying fractions, it isn't hard to teach that 1 divided by 3/4, say, is 4/3, since it is easily shown that 3/4 x 4/3 = 1.<BR/><BR/>Once that is mastered, they move on and a problem like 2/3 divided by 1/2 is explained. They start out similarly to what you do: i.e., how many 1/2's are in 2/3? They then shift and say, well let's first find out how many 1/2's are in 1? That would be 1 divided by 1/2 which is 2. We know there are 2 1/2's in 1, so now we want to know how many are in 2/3. Since 2/3 is 2/3 of 1, and there are 2 1/2's in 1, we take 2/3 of 2 or 2/3 x 2.Barry Garelickhttps://www.blogger.com/profile/01281266848110087415noreply@blogger.com